Author(s): KW Bunonyo and L Ebiwareme

Abstract: This research involves three propositions. First, we proposed a model that represents tumor growth caused by carcinogenic substances from an initially diagnosed level; secondly, we proposed several therapeutic models for chemotherapy, immunotherapy, and radiotherapy, respectively, with a steady supply of dosage, with the aim of solving the cell proliferation issue. Thirdly, we modified the tumor growth model where we considered the therapeutic effect on the tumor cell with several interactive terms. The proposed models were solved analytically where tumor cell functions with and without therapeutic effects were obtained. On the other hand, we obtained independent solutions of chemotherapy, immunotherapy, and radiotherapy functions were also obtained, with some pertinent parameters. We developed numerical simulation codes using Wolfram Mathematica software, version 12 to simulate the various functions by varying the pertinent parameters to study their effect on tumor growth and to study each significant level. Numerical simulation was carried out, and it was observed that continuous exposure to radiation could cause pain and normal cell death, thereby supporting the tumor cell proliferation, but the chemotherapeutic and immunotherapeutic drugs help in shrinking the tumor and reducing cell proliferation. The simulated results for the mixed treatment application for all therapies indicate that there is a successful and faster decrease in tumor size by combining the treatment regimes. In conclusion, we have successively proposed and solved mathematical models that represent tumor growth without treatment and with the application of treatment. The models in this article can be used by scientists and oncologists in studying tumor cell proliferation.

DOI: 10.22271/maths.2022.v7.i2b.806

Pages: 123-132 | Views: 438 | Downloads: 21

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